Let \(a, b \in R\) be such that the equation \(a x^2-2 b x+15=0\) has a repeated root \(\alpha\). If \(\alpha\) and \(\b…

Let \(a, b \in R\) be such that the equation \(a x^2-2 b x+15=0\) has a repeated root \(\alpha\). If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-2 b x+21=0\), then \(\alpha^2+\beta^2\) is equal to:

[JEE Main 2022, 25 Jun (Shift 2)]